Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4

A. C. Petkou; G. Arutyunov; S. Frolov

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Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4

G. Arutyunov, S. Frolov, A. C. Petkou

High Energy Physics - Theory · Submitted 17 Oct 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.

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arXiv IDhep-th/0010137 (version 2)

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CitationA. C. Petkou, G. Arutyunov, S. Frolov. "Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4." arXiv:hep-th/0010137 (2000). https://pith.science/paper/VRTANG2F

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.72 · mentions code or data availability 0.02.

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We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4.	contribution 0.99	0.92	0.06	asserted 0.70
s1	We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions.	result 0.99	0.82	0.22	asserted 0.84
s2	We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively.	result 0.94	0.93	0.22	asserted 0.99
s3	The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling.	result 1.00	0.82	0.18	asserted 1.00
s4	For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.	result 1.00	0.94	0.26	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Original abstract

We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.

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References

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The ${\cal N} = 8$ Superconformal Bootstrap in Three Dimensions
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Unitarity plus crossing symmetry, applied to the four-point function of the N=8 stress-tensor multiplet, yields numerical bounds on 3d N=8 SCFTs that nearly saturate at the free U(1)xU(1) and large-N ABJM theories.
An Index for 4 dimensional Super Conformal Theories
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A supersymmetric index for four dimensional superconformal theories is defined, shown to capture all group-theoretically protected states, and computed for N=4 Yang Mills with exact agreement between the weak-coupling...
Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
hep-th 2001-12 accept novelty 7.0 of 10

Superconformal symmetry fixes the four point function of chiral primary operators up to one function of two variables, and the paper uses this to write the operator product expansion in terms of complete supermultiplets.
Lessons from crossing symmetry at large N
hep-th 2014-10 conditional novelty 6.0 of 10

At large N and large coupling, crossing symmetry admits the supergravity solution plus an infinite tower of extra solutions, which the authors argue are suppressed by a gap scale of order N^(1/4).
Superconformal Ward Identities and their Solution
hep-th 2004-07 accept novelty 6.0 of 10

The authors derive superconformal Ward identities for four-point functions of arbitrary-rank chiral primary operators in N=2 and N=4 theories and solve them in a form that maps cleanly onto long, short, and semi-short...

Show 2 more citing papers

On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
hep-th 2002-09 accept novelty 6.0 of 10

At the unitarity threshold a long superconformal multiplet decomposes into four semi-short multiplets, and only the 1/2-BPS [0,p,0] and 1/4-BPS [1,p,1] multiplets are guaranteed to have protected scale dimensions.
Supersymmetric Gauge Theories and the AdS/CFT Correspondence
hep-th 2002-01 accept novelty 2.0 of 10

A pedagogical review that builds N=4 SYM, Type IIB supergravity, and D3-branes from scratch and then works out how AdS/CFT computes correlation functions and holographic RG flows.

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6 arXiv papers cite this in 7 sentences

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Papers citing it · 3 sentences without a confident label

Uses its data or values 1 paper

Its one-loop anomalous dimension is $Δ^(1)=3λ/4^2$ [ref] .

Circular Wilson loops in defect ${\cal N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion · Operator product expansion expansion of the Wilson loop · 0.92

Cites it as background 2 papers

[ref] , and is contained in the $O_2^2 O_2^2$ OPE.

Four-point correlators with BPS bound states in AdS$_3$ and AdS$_5$ · $⟨O_2^2 O_2^2 O_2 O_2 ⟩$ and the twist two sector · 0.97
For more information on the issue, see [ref] as an original related study and look, for instance, at [ref] , [ref] for non-renormalization theorems and corrections for operators and multi-point correlation functions of gauge-invariant composite operators in AdS$_5$/CFT$_4$ correspondence.

Non-Minimally Coupled Pseudoscalars in AdS_4 for Instantons in CFT_3 · Further Discussions · 0.98

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